Oliva Zapata, Julio EduardoConcha Aguilera, Patrick KeissyGallegos Pastén, Eduardo2026-04-272026-04-272026https://repositorio.udec.cl/handle/11594/13965Tesis presentada para optar al grado de Magíster en Ciencias con mención en Física.In this thesis, we present a Maxwell extension of the kinematical Lie algebras by promoting the Bacry–Lévy-Leblond cube to a semigroup expansion framework. Within this approach, we show that both non- and ultra-relativistic Maxwell algebras admitting nondegenerate invariant bilinear forms can be systematically obtained from different parent algebras through a unified expansion scheme, leading to a Maxwellian kinematical cube. We further show that both the original Bacry–Lévy-Leblond cube and its Maxwellian extension belong to an infinite hierarchy of generalized kinematical algebras generated by higher-order semigroups. The expansion method naturally provides the corresponding invariant tensors, allowing for the systematic construction of three-dimensional Chern–Simons gravity theories.enCC BY-NC-ND 4.0 DEED Attribution-NonCommercial-NoDerivs 4.0 InternationalAlgebraGravityThesis